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Bilevel subsidy-enabled mobility hub network design with perturbed utility coalitional choice-based assignment

Hai Yang, Joseph Y. J. Chow

TL;DR

The paper tackles the challenge of designing subsidy-enabled mobility hubs within a Mobility-as-a-Service framework by formulating a bilevel model where a central platform sets traveler-facing prices and operator subsidies, while a lower-level PURC-based assignment captures the joint traveler–operator coalitional decisions. By reformulating the bilevel problem with KKT conditions and solving via a gap-penalty method with iterative warm-starts, the approach achieves high-quality solutions at realistic scales. The methodology is validated on a toy network and a large Long Island Rail Road (LIRR) case, revealing that MHs can significantly reduce travel disutility and that link-based subsidies offer granular control, with hub-based subsidies offering a different trade-off in computational effort and policy interpretation. The results provide actionable insights for policymakers and operators, such as the social surplus value of MHs, the impact of subsidy caps, and the importance of competition, while outlining avenues for extending the framework to richer supply-side dynamics and broader applications.

Abstract

Urban mobility is undergoing rapid transformation with the emergence of new services. Mobility hubs (MHs) have been proposed as physical-digital convergence points, offering a range of public and private mobility options in close proximity. By supporting Mobility-as-a-Service, these hubs can serve as focal points where travel decisions intersect with operator strategies. We develop a bilevel MH platform design model that treats MHs as control levers. The upper level (platform) maximizes revenue or flow by setting subsidies to incentivize last-mile operators; the lower level captures joint traveler-operator decisions with a link-based Perturbed Utility Route Choice (PURC) assignment, yielding a strictly convex quadratic program. We reformulate the bilevel problem to a single-level program via the KKT conditions of the lower level and solve it with a gap-penalty method and an iterative warm-start scheme that exploits the computationally cheap lower-level problem. Numerical experiments on a toy network and a Long Island Rail Road (LIRR) case (244 nodes, 469 links, 78 ODs) show that the method attains sub-1% optimality gaps in minutes. In the base LIRR case, the model allows policymakers to quantify the social surplus value of a MH, or the value of enabling subsidy or regulating the microtransit operator's pricing. Comparing link-based subsidies to hub-based subsidies, the latter is computationally more expensive but offers an easier mechanism for comparison and control.

Bilevel subsidy-enabled mobility hub network design with perturbed utility coalitional choice-based assignment

TL;DR

The paper tackles the challenge of designing subsidy-enabled mobility hubs within a Mobility-as-a-Service framework by formulating a bilevel model where a central platform sets traveler-facing prices and operator subsidies, while a lower-level PURC-based assignment captures the joint traveler–operator coalitional decisions. By reformulating the bilevel problem with KKT conditions and solving via a gap-penalty method with iterative warm-starts, the approach achieves high-quality solutions at realistic scales. The methodology is validated on a toy network and a large Long Island Rail Road (LIRR) case, revealing that MHs can significantly reduce travel disutility and that link-based subsidies offer granular control, with hub-based subsidies offering a different trade-off in computational effort and policy interpretation. The results provide actionable insights for policymakers and operators, such as the social surplus value of MHs, the impact of subsidy caps, and the importance of competition, while outlining avenues for extending the framework to richer supply-side dynamics and broader applications.

Abstract

Urban mobility is undergoing rapid transformation with the emergence of new services. Mobility hubs (MHs) have been proposed as physical-digital convergence points, offering a range of public and private mobility options in close proximity. By supporting Mobility-as-a-Service, these hubs can serve as focal points where travel decisions intersect with operator strategies. We develop a bilevel MH platform design model that treats MHs as control levers. The upper level (platform) maximizes revenue or flow by setting subsidies to incentivize last-mile operators; the lower level captures joint traveler-operator decisions with a link-based Perturbed Utility Route Choice (PURC) assignment, yielding a strictly convex quadratic program. We reformulate the bilevel problem to a single-level program via the KKT conditions of the lower level and solve it with a gap-penalty method and an iterative warm-start scheme that exploits the computationally cheap lower-level problem. Numerical experiments on a toy network and a Long Island Rail Road (LIRR) case (244 nodes, 469 links, 78 ODs) show that the method attains sub-1% optimality gaps in minutes. In the base LIRR case, the model allows policymakers to quantify the social surplus value of a MH, or the value of enabling subsidy or regulating the microtransit operator's pricing. Comparing link-based subsidies to hub-based subsidies, the latter is computationally more expensive but offers an easier mechanism for comparison and control.

Paper Structure

This paper contains 20 sections, 4 theorems, 17 equations, 10 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. MaaS platform models
  4. Mobility Hubs
  5. Research gaps and our contributions
  6. Proposed mobility hub platform design methodology
  7. Network structure and model assumptions
  8. Lower-level traveler-operator coalition choice assignment model using PURC based structure
  9. Upper level model formulation
  10. Solution method
  11. Numerical experiments
  12. Illustrative example
  13. LIRR mobility hubs case study
  14. Base case
  15. MOD link operating cost sensitivity analysis
  16. ...and 5 more sections

Key Result

Proposition 1

The first and second terms combined in Eq. (eq:service_model_obj) are equivalent to the PURC objective proposed by fosgerau2022perturbed.

Figures (10)

  • Figure 1: Network illustration for one OD pair
  • Figure 2: Toy network illustration
  • Figure 3: LIRR network illustration: (a) map of LIRR from the MTA with the three stations circled in red; (b) overlay of the census tracts within 5 miles of those stations; and (c) the MaaS subnetwork with links connecting each census tract to nearby stations
  • Figure 4: Convergence between single level objective and true platform profit.
  • Figure 5: Mode share of MH based MOD services.
  • ...and 5 more figures

Theorems & Definitions (12)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • Remark 1
  • Remark 2
  • ...and 2 more